Combining Texts

All the ideas for 'Rule Utilitarianism and Euthanasia', 'Mathematics without Numbers' and 'A Completeness Theorem in Modal Logic'

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11 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]
The Barcan formulas fail in models with varying domains [Kripke, by Williamson]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
Rule-utilitarians prevent things like torture, even on rare occasions when it seems best [Hooker,B]
25. Social Practice / F. Life Issues / 2. Euthanasia
Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B]
Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B]